ROZIKOV Utkir

Non-linear Dynamical Systems: Evolution of Sex-linked Populations and Thermodynamics of Spin Systems Related to the Physics on Graphs

Summary of the research project:

The project has two directions:

A. The first direction will be devoted to dynamical systems, social networks, disease propagation in populations and evolution algebras (genetic, algebras of free and bisexual population etc.) and their applications to population biology. We will study non-archimedean (p-adic) analogies of the biological systems and apply the results to the theory of cataclysm (catastrophe).

B. The project is also aimed at studying the thermodynamics (in physics and biology) and pure phases (extreme Gibbs measures) of several spin systems on graphs. We will also apply the theory of Gibbs measures to the fields of neural and communication networks. Moreover, we will study phase transition problems of spin systems over the field of p-adic numbers.